Bounding convergence rates for Markov chains: An example of the use of computer algebra

John E. Kolassa

doi:10.1023/A:1026566101230

Bounding convergence rates for Markov chains: An example of the use of computer algebra

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Abstract

Kolassa and Tanner (J. Am. Stat. Assoc. (1994) 89, 697-702) present the Gibbs-Skovgaard algorithm for approximate conditional inference. Kolassa (Ann Statist. (1999), 27, 129-142) gives conditions under which their Markov chain is known to converge. This paper calculates explicity bounds on convergence rates in terms calculable directly from chain transition operators. These results are useful in cases like those considered by Kolassa (1999).

Original language	English (US)
Pages (from-to)	83-87
Number of pages	5
Journal	Statistics and Computing
Volume	11
Issue number	1
DOIs	https://doi.org/10.1023/A:1026566101230
State	Published - 2001

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Statistics and Probability
Statistics, Probability and Uncertainty
Computational Theory and Mathematics

Keywords

Computer algebra
Markov chain
Monte Carlo

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title = "Bounding convergence rates for Markov chains: An example of the use of computer algebra",

abstract = "Kolassa and Tanner (J. Am. Stat. Assoc. (1994) 89, 697-702) present the Gibbs-Skovgaard algorithm for approximate conditional inference. Kolassa (Ann Statist. (1999), 27, 129-142) gives conditions under which their Markov chain is known to converge. This paper calculates explicity bounds on convergence rates in terms calculable directly from chain transition operators. These results are useful in cases like those considered by Kolassa (1999).",

keywords = "Computer algebra, Markov chain, Monte Carlo",

author = "Kolassa, {John E.}",

note = "Funding Information: The author gratefully acknowledged suggestions from M. Tanner, Y. Seifu, J. Rosenthal, W. Kendall, J. Stafford, and two anonymous referees. Supported by grants CA 63050 and CA 35464 from the National Institutes of Health.",

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N2 - Kolassa and Tanner (J. Am. Stat. Assoc. (1994) 89, 697-702) present the Gibbs-Skovgaard algorithm for approximate conditional inference. Kolassa (Ann Statist. (1999), 27, 129-142) gives conditions under which their Markov chain is known to converge. This paper calculates explicity bounds on convergence rates in terms calculable directly from chain transition operators. These results are useful in cases like those considered by Kolassa (1999).

AB - Kolassa and Tanner (J. Am. Stat. Assoc. (1994) 89, 697-702) present the Gibbs-Skovgaard algorithm for approximate conditional inference. Kolassa (Ann Statist. (1999), 27, 129-142) gives conditions under which their Markov chain is known to converge. This paper calculates explicity bounds on convergence rates in terms calculable directly from chain transition operators. These results are useful in cases like those considered by Kolassa (1999).

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KW - Markov chain

KW - Monte Carlo

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Bounding convergence rates for Markov chains: An example of the use of computer algebra

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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